Weakly c-permutable subgroups of finite groups

Abstract

A subgroup H of a group G is called weakly c -permutable in G if there exists a subgroup T of G such that G = H T and H ∩ T is completely c -permutable in G . In this paper, we obtain some results about the weakly c -permutable subgroups and use them to determine the structures of some groups. In particular, we give some new characterizations of supersolvability and p -nilpotency of a group (and, more general, a group belonging to a given formation of finite groups) by using the weakly c -permutability of some primary subgroups. As application, we generalize a series of known results.